Variation and inverses
If
y=5x
, what type of variation is shown?
Direct Variation
What value of x makes the denominator of
f(x)=1/(x-6)
undefined?
6
Simplify:
\frac{3}{x}+\frac{3}{x}
\frac{6}{x}
Solve:
\frac{2}{x} = \frac{4}{6}
x=3
“Have it your way” is the memorable slogan of what fast food restaurant?
Burger King
A table shows that when x increases by one, y becomes one-fourth as large. What type of variation is this?
Inverse Variation
State the vertical and horizontal asymptotes of
f(x)=\frac{2}{x+1}+4
VA: x=−1, HA: y=4
\frac{x}{x+5}*\frac{2x}{x-5} .
\frac{2x^2}{x^2-25}
\frac{x}{x+2} = \frac{3}{5}
x=3
In 1994, WIRED magazine described this 4-letter word as an idea leaping “from mind to mind … as viruses leap from body to body.”
What is a meme?
Does the equation
xy=20
represent direct variation, inverse variation, or neither?
Inverse variation
If a rational function has a vertical asymptote at x=−3, name one possible function.
\frac{**}{x+3}
\frac{5x}{x^2}-\frac{1}{x}
\frac{4x}{x^2}
Identify the LCD
\frac{4}{x+9}+\frac{3x}{2x-1}=\frac{10}{3}
3(x+9)(2x-1)
In the song “Santa Baby,” the singer asks for a deed to what?
A platinum mine
Find the inverse of
f(x)=2x+5
f^(−1)(x)=\frac{x-5}{2}
Give the domain of
f(x)=\frac{4x}{x^2-9}
All real
x ≠ 3 , − 3
\frac{6x}{x^2-4}÷\frac{x+2}{3}
\frac{18x}{x+2}
\frac{2}{3x}+\frac{1}{6}=\frac{4}{3x}
x=4
In 1984, in the first of the films featuring this character, he only has 21 lines, for a total of 133 words.
Who is The Terminator?
Find the inverse of the rational function
f(x)=\frac{4x-1}{x+2}
f(x)=\frac{2x-1}{x-4}
Describe the transformations needed to turn \frac{1}{x} into the graph of
g(x)=\frac{-3}{x+2}-1
Reflection over x-axis, vertical stretch by 3, left 2, down 1
\frac{x}{x^2-1}+\frac{3}{x+1}
\frac{4x-3}{x^2-1}
Solve for x.
\frac{x}{x+4}=\frac{16}{x^2+4x}+\frac{2}{x}
x=6
Research for rubber substitutes during World War 2 lead to the creation of this famous children's toy.
Silly putty